The purpose of a Cooldown Reduction (CDR) hat on Evan is to reduce the cooldown of Mir Skills (Dragon Flash, Dive, Breath, and Slam) which in turn, reduces the cooldown of fusion skills. It also affects the timing of activating Freud's Wisdom, HEXA Elemental Barrage, Wyrmking's Breath, Blink and Ethereal Form.
CDR Hat has been significantly more impactful after GMS v.263 reduced Dragon Slam's cooldown and adjusted cooldowns to a 2-minute meta.
Heroic
Regular three-line roll goal: -2 second CDR w/ 20% INT
Keep the first of these two double-prime rolls that you encounter.
-2 second CDR w/ 23% INT
-4 second CDR w/ 10% INT
Interactive
From strongest to weakest (including bonus potential):
-5 second CDR
-4 second CDR
-2 second CDR